This work stands somewhat apart in El Niño dynamics research: nearby studies include those on delays that trigger rhythms, the thermal pump of Enceladus's ocean, pressure in superconductors, the magnetic key in the helix of life, the quantum lace of gravity, noise generating order, predicting El Niño a year and a half ahead, and the mirror crack of neutrinos. Most neighbors consider either a single oscillator with noise or global climate effects. This article stands out by modeling the interaction of two deterministic ocean subregions with different parameters, which had not been systematically studied in the El Niño context before.
The authors construct a system of two coupled delay differential equations for sea surface temperature anomalies in two subregions. Each region is described by a delayed oscillator model: positive feedback through advection, cubic damping, and delayed negative feedback reflecting the transit time of equatorial Kelvin and Rossby waves across the basin. Coupling between regions is linear and models energy flux across the shared boundary. Cases of identical and nonidentical subregions (different self-delay strengths and delays) are studied. Analysis includes constructing phase diagrams, stability analysis of fixed points via the Jacobian, assessing basin stability, and computing synchronization error.
For identical subregions with weak interregional coupling, coexistence of amplitude and oscillation death is observed at small delays, and heterogeneous oscillations at large delays. For moderate coupling, homogeneous oscillations arise for sufficiently large delays, and amplitude death for small delays. Strong coupling completely suppresses oscillations. Large self-delay strengths promote oscillations, while weak delayed coupling quenches them, confirming the key role of oceanic waves in ENSO genesis. For nonidentical subregions, oscillation death and heterogeneous oscillations dominate, unlike the homogeneous case. Under weak coupling, a region with a large delay can induce oscillations in a region that would otherwise settle to a steady state in isolation. The oscillation period increases with delay and is the same for both regions even when parameters differ.
The work shows that deterministic coupling between ocean subregions can generate complex irregular patterns qualitatively similar to observed ENSO data, without the need for external noise. This contrasts with common stochastic extensions of the recharge oscillator, where irregularity is introduced by noise. The model offers a mechanism for synchronization or its absence in temperature anomalies across different regions and emphasizes that strong coupling suppresses oscillations, while weak coupling of nonidentical regions can amplify them.
The topic could develop toward including more subregions, accounting for spatial heterogeneity of parameters, and comparing with real sea surface temperature time series in different longitudinal bands. It may also explore the influence of network topology on collective oscillations and transitions to synchronization. Additionally, studying the role of nonlinear coupling forms and state-dependent delays is promising.
The results may be useful for climatologists studying regional ENSO manifestations and their interconnections, as well as for specialists in nonlinear dynamics of coupled systems with delays.
The next step could be calibrating model parameters against observational data for specific pairs of equatorial Pacific regions and testing predictions about synchronization. It is also worth investigating the influence of noise on the identified deterministic regimes.
The work addresses a fundamental problem in climatology: to what extent El Niño irregularity is due to internal ocean-atmosphere dynamics versus external noise. It shows that heterogeneity and coupling of subregions can by themselves create complex temporal patterns, raising questions about ENSO predictability limits.
Since 1899, 29 El Niño events have been recorded, giving an average period of about 3.7 years, though intervals range from two to seven years.